If you're talking as in having relatives, I have this to say: it seems as though in past Zelda games, Link has gradually gained more family as more story space has opened up. In Legend of Zelda and Adventure of Link, he was a loner with no background. Then comes A Link to the Past, and he has an uncle that he lives with. Ocarina of Time, he had a mother that died when he was an infant. Wind Waker, he had a grandmother and sister. Twilight Princess, I'm not sure if they talked much about his parents. Spirit Tracks, nothing much is known, but we had Niko, and he was like family to Link in Wind Waker and Phantom Hourglass.
I suppose that, as more Zelda games go along, Link's background and life is explained more in detail. I'd see Link with family members, but perhaps not his biological parents. Maybe having something similar where Link is taken in after his parents die or something (and perhaps going into detail with his past experiences that he, for some reason, could not remember) would be interesting. We aren't so used to having Link be with family members. I mean, Aryll was gone about 90% of Wind Waker, seeing her only in the beginning, middle, end, and letters throughout the game. Link's Uncle in A Link to the Past is gone for 99% of the game, being seen only in the beginning and end. Link's mother in Ocarina of Time isn't seen at all, and no family is spoken about in Twilight Princess, Spirit Tracks, and the NES Zeldas.
Now, if you're talking about having a family (wife, kids) and not just having family members, that would be pretty much why the end of every Zelda game somewhat dissapoints me. I mean, Link met all of these people he could hang out with, but he just leaves it all to waste in exchange for something else, even though he's seen all of Hyrule and met everyone. It would be interesting for him to have a family, but to have one in the game, that wouldn't be great. In addition, while the life expectancy of the Middle Ages wasn't that high, by his looks, he appears far too young to be raising a family.